I think the question is either written wrong

g(x) = (x^2+2)/(x-1)

Please use parenthesis while typing questions .. you need to know the fundamentals of algebra ... If you are absolutely new to Algebra.. it might not be a bad idea to pick up one of the many course materials offered by Kaplan, MGMAT and the like..

- pradeep

vladmire wrote:For all numbers x such that x does not equal 1, if g(x) is defined
by g (x) = x^2 + 2/x-1, then (1/g(2)) (1/g(x)) =

6(x-1)/x^2+2

x-1/6(x^2+2)

x^2+2/ 6(x-1)


What basics do I need to know to figure this out?

I would simplify and plug numbers. Solving algebraically each one will take too long!!

g(2) = 8 (just plug in x=2 for g(2))

1/g(2) * 1/g(x) = 1/8 * 1/g(x) = h(x)

lets see with x=3 (arbitrary number)

h(3) = 1/8 * 1/g(3) = 1/24

So one of the choices should equal 1/24 with x=3
if there is more than one you should pick another number besides x=3.

i`m not getting them to be equal..can someone help

see attached sry

that's much better, thanks for the attachment.

THe answer should be "D"

you solve one at a time.

when x = 2, then g(2) = ....

you plug in 2 for x, then you get 6.

g(x) is already given.

Now the question asks for 1/(g(2)) times 1(g(x))

you simply take the reciprocal of that and multiply them together.

rec. of 6 = 1/6 times rec of (x^2 + 2)/(x-1) = (x-1)/(x^2 + 2)
multiply together, you have (x-1) / 6(x^2 + 2)

answer, D

is that the OA?

yes it is D

rec. of 6 = 1/6 times rec of (x^2 + 2)/(x-1) = (x-1)/(x^2 + 2)
multiply together, you have (x-1) / 6(x^2 + 2)

I understand all the way up until getting (x-1)/6(x^2+2) why is the 6 under the division sign instead of 6(x-1)/(x^2+2)

vladmire wrote:

rec. of 6 = 1/6 times rec of (x^2 + 2)/(x-1) = (x-1)/(x^2 + 2)
multiply together, you have (x-1) / 6(x^2 + 2)

I understand all the way up until getting (x-1)/6(x^2+2) why is the 6 under the division sign instead of 6(x-1)/(x^2+2)

if you solve the original equation with x=2, then you get the value of 6.

But that's not what the question is asking. question asks

what is 1 / (g(x)) times 1 / (g(2))

we know that g(2) is 6 because we solved the equation using x=2.

so 1 divided by g(2) is 1/6. does that clear things up?

i sometimes wished we had a drawing board... so much easier to write.

when you solve these two equations, solve them separately so you won't get mixed up. you'll be able to see it clearly.

its pretty simple
put x =2 in g(x) & g(2) = 6
and dont do any thing for 1/g(x)

So, putting back it ll be (1/6)(x-1)/((x^2+2)
Hence D.